The scaling law for the strain dependence of the critical current density in Nb₃Sn superconducting wires

TLDR

The authors aim to establish a universal strain‑dependent relation for Nb₃Sn wires and propose a general scaling law for JC(B,T,εI). They performed comprehensive measurements of JC versus magnetic field, temperature, and axial strain on internal‑tin and bronze‑route Nb₃Sn wires and developed a scaling law grounded in microscopic theory and phenomenology. The results show JC follows thermodynamic variables, reveal a power‑law BC₂*–strain relation with exponent ~2.2, indicate strain mainly alters phononic properties, and that the new scaling law predicts JC within ~4 % accuracy, outperforming the Summers law.

Abstract

Comprehensive measurements are reported of the critical current density (JC) of internal-tin and bronze-route Nb3Sn superconducting wires as a function of magnetic field (B≤23 T), temperature (4.2 K ≤T≤12 K) and axial strain (−1.6%≤εI≤0.40%). Electric field–temperature characteristics are shown to be equivalent to the standard electric field–current density characteristics to within an experimental uncertainty of ∼20 mK, implying that JC can be described using thermodynamic variables. We report a new universal relation between normalized effective upper critical field (BC2*(0)) and strain that is valid over a large strain range for Nb3Sn wires characterized by high upper critical fields. A power-law relation between BC2*(0,εI) and TC*(εI) (the effective critical temperature) is observed with an exponent of ∼2.2 for high-upper-critical-field Nb3Sn compared to the value ≥3 for binary Nb3Sn. These data are consistent with microscopic theoretical predictions and suggest that uniaxial strain predominantly affects the phononic rather than the electronic properties of the material. The standard Summers scaling law predicts a weaker strain dependence than is observed. We propose a scaling law for JC(B,T,εI) based on microscopic theory and phenomenological scaling that is sufficiently general to describe materials with different impurity scattering rates and electron–phonon coupling strengths. It parametrizes complete datasets with a typical accuracy of ∼4%, and provides reasonable predictions for the JC(B,T,εI) surface from partial datasets.